Re: Re: Holes when plotting funtions
- To: mathgroup at smc.vnet.net
- Subject: [mg42200] Re: [mg42194] Re: Holes when plotting funtions
- From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
- Date: Mon, 23 Jun 2003 05:49:41 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
Roman Maeder's article deals with (among other things) detecting singularities. However, in this case there is no singularity: In[19]:= Limit[x(1-Cos[x])/(x-Sin[x]),x->0] Out[19]= 3 If you try Maeder's IntervalPlot on this graph you will get something rather surprising and very far from what was asked for. In fact Mathematica's interval arithmetic doesn't seem to be able to deal with this function properly, try: Function[x, x(1-Cos[x])/(x-Sin[x]][Interval[-1,1]] Andrzej Kozlowski Yokohama, Japan http://www.mimuw.edu.pl/~akoz/ http://platon.c.u-tokyo.ac.jp/andrzej/ On Sunday, June 22, 2003, at 05:05 PM, Bill Rowe wrote: > On 6/21/03 at 8:57 PM, Elansary at btopenworld.com (Ashraf El Ansary) > wrote: > >> Is there any way to mathematica to distinguish non-continous >> equations in >> the 'Plot' function. For example: >> f[x_]:=x(1-Cos[x])/(x-Sin[x]) >> Plot[f[x],{x,-20,20},AxesLabel->{x,y},AxesOrigin->{0,0}] > >> The above example is not defined around zero, but when plotted by >> Mathematica , it looks as if the function is continous. Is there any >> way to >> plug a whole in those intervals which are not continous (simillar to >> those >> depicted in textbooks for step /open/closed intervals]...... > > Roman Maeder wrote an article for the Mathematica Journal (vol 7.3) > regarding interval plots that identifies problems like this. If you > have a subscription to the Mathematica Journal you can download the > this artical in electronic format from their web site. If not, try a > search on the Wolfram Information Center. Look for articles written by > Roman Maeder on the subject of interval plots or global optimization > > >